Area of greatest Overturning Moment.—Although the rate of dissipation of the impulsive effects of an earthquake may follow a law like that just enumerated, it must be remembered that if the depth of the origin is comparable with the radius of the area which is shaken, the maximum impulsive effect as exhibited by the actual destruction on the surface may not be immediately above the origin where buildings have simply been lifted vertically up and down, but at some distance from this point, where the impulsive effort has been more oblique.
At the epicentrum we have the maximum of the true intensity as measured by the acceleration of a particle, or the height to which a body might be projected, but it will be at some distance from this where we shall have the maximum intensity as exhibited by an overturning effort.
This will be rendered clear by the following diagram.
In the accompanying diagram let o be the origin of a shock, and o c the seismic vertical equal to r. Let the direct or normal shock emerge at c, c1, c2, and at the angles θ1, θ2, &c.
Assuming that the displacement of an earth particle at c equals c b, and at c1 equals c1 b1, and at c2 equals c2 b2, &c., and let these displacements c b, c1 b1, c2 b2, &c., for the sake of argument, vary inversely as r, r1, r2, &c.
Fig. 9.
The question is to determine where the horizontal component c a of these normal motions is a maximum.
First observe that the triangle o c c is similar to a, b, c.
Also r = h/sin θ, and therefore the normal component c1 b1 at c1 is equal to c sin θ/h.